Problem: Gabriela is 2 times as old as Christopher. 42 years ago, Gabriela was 9 times as old as Christopher. How old is Gabriela now?
Explanation: We can use the given information to write down two equations that describe the ages of Gabriela and Christopher. Let Gabriela's current age be $g$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $g = 2c$ 42 years ago, Gabriela was $g - 42$ years old, and Christopher was $c - 42$ years old. The information in the second sentence can be expressed in the following equation: $g - 42 = 9(c - 42)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = g / 2$ . Substituting this into our second equation, we get: $g - 42 = 9($ $(g / 2)$ $- 42)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 42 = \dfrac{9}{2} g - 378$ Solving for $g$ , we get: $\dfrac{7}{2} g = 336$ $g = \dfrac{2}{7} \cdot 336 = 96$.